Question

In the following exercises, perform indicated operations.

$\frac{4}{s-7}+\frac{5}{s+3}$

Short answer

The resultant expression is$\frac{9s-23}{(s-7)(s+3)}$.

Step-by-step solution

Step 1. Given Information

The given expression is$\frac{4}{s-7}+\frac{5}{s+3}$.

Step 2. Express with common denominator

• The LCD of the terms of given expression is $(s-7)(s+3)$.
• Multiply the numerator and denominator of first term by $(s+3)$and second term by $(s-7)$.

role="math" localid="1645165764841" $\frac{4(s+3)}{(s-7)(s+3)}+\frac{5(s-7)}{(s+3)(s-7)}=\frac{4s+12}{(s-7)(s+3)}+\frac{5s-35}{(s+3)(s-7)}$

Step 3. Simplify

• As the denominator is the same for both the terms, perform addition in the numerator and place it over the common denominator.

$\frac{4s+12+5s-35}{(s-7)(s+3)}=\frac{9s-23}{(s-7)(s+3)}$

• So, the resultant expression is$\frac{9s-23}{(s-7)(s+3)}$.